Explaining D6 add 9

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Your guitar is in standard tuning.

Place your fingers on the second frets of the bottom E string and the G string.  Strum all six strings.  You have a D6add9 chord.

The bottom four strings produce a D major chord.  The open B string provides the sixth note in a D major chord, making it a D6 chord.

I wondered why it is not called a D6add2, because the open E string provides the second note in the major scale.  But of course the ninth note is also the second note, just an octave higher.

The E in the D6add9 comes from the top E string.  It is the highest pitched note in the chord, and presumably that is why it is called D6add9 rather than D6add2.

Am I right?
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